*3.2. Final Forecasting Step*

In the primary forecasting step, variables were selected by the NSGAII and an output was generated which is an MLPNN with selected input vector. As the final step, output of the MLPNN was fed into the created ANFIS models with different training algorithms, to evaluate the ability of the ANFIS to increase the forecasting results of the MLPNN model. The results are given in Table 3.


**Table 3.** Forecasting results for each model.

As seen in Table 3, the combination of the MLPNN and ANFIS models improves the forecasting accuracy and MLPNN-ANFIS models and demonstrates lower error rates compared to the MLPNN and ANFIS models. Furthermore, all error indicators of RMSE, MAE, MAPE, and R related to MLPNN-ANFIS-GA model are lower than MLPNN-ANFIS-GA model. Thus, GA has a better performance in ANFIS training compared to the hybrid method. Figure 9 presents the errors and absolute percentage error (APE) for ANFIS-GA and MLPNN-ANFIS-GA models to better demonstrate the increased forecasting accuracy using a combination of MLPNN and ANFIS.

**Figure 9.** Errors and APE (%) for ANFIS-GA and MLP-ANFIS-GA models.

For the purposes of better illustrating the accuracy of the tested models, error indication of the correlation coefficient for MLPNN, ANFIS-Hybrid, ANFIS-GA, and MLPNN-ANFIS-GA models are presented in Figure 10 while error indicators for these models are presented in Table 4.

**Table 4.** Error indicators for MLPNN, ANFIS-Hybrid, ANFIS-GA, and MLPNN-ANFIS-GA models using the selected input vector by NSGAII.


**Figure 10.** Correlation coefficient for MLPNN, ANFIS-Hybrid, ANFIS-GA, and MLPNN-ANFIS-GA models.

As seen, the MLPNN-ANFIS-GA model provides the best correlation coefficient and lower error rates in terms of the RMSE, MAE, and MAPE among the tested models. The targets (actual load) and the final forecasting results for a one-day region and a one-week region are presented in Figures 11 and 12 respectively.

**Figure 11.** Forecasting results for a one-day region.

**Figure 12.** Forecasting results for a one-week region.
